posic/talks/mpi_app.tex

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  42 \usepackage{semlayer}           % Seminar overlays
  43 \usepackage{slidesec}           % Seminar sections and list of slides
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  81 \begin{document}
  82
  83 \extraslideheight{10in}
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  85
  86 \pagestyle{empty}
  87
  88 % specify width and height
  89 \slidewidth 26.3cm
  90 \slideheight 19.9cm
  91
  92 % margin
  93 \def\slidetopmargin{-0.15cm}
  94
  95 \newcommand{\ham}{\mathcal{H}}
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  99
 100 % itemize level ii
 101 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
 102
 103 % nice phi
 104 \renewcommand{\phi}{\varphi}
 105
 106 % roman letters
 107 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
 108
 109 % colors
 110 \newrgbcolor{si-yellow}{.6 .6 0}
 111 \newrgbcolor{hb}{0.75 0.77 0.89}
 112 \newrgbcolor{lbb}{0.75 0.8 0.88}
 113 \newrgbcolor{hlbb}{0.825 0.88 0.968}
 114 \newrgbcolor{lachs}{1.0 .93 .81}
 115
 116 % shortcuts
 117 \newcommand{\si}{Si$_{\text{i}}${}}
 118 \newcommand{\ci}{C$_{\text{i}}${}}
 119 \newcommand{\cs}{C$_{\text{sub}}${}}
 120 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
 121 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
 122 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
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 124
 125 % no vertical centering
 126 %\centerslidesfalse
 127
 128 % layout check
 129 %\layout
 130 \begin{slide}
 131 \center
 132 {\Huge
 133 E\\
 134 F\\
 135 G\\
 136 A B C D E F G H G F E D C B A
 137 G\\
 138 F\\
 139 E\\
 140 }
 141 \end{slide}
 142
 143 % topic
 144
 145 \begin{slide}
 146 \begin{center}
 147
 148  \vspace{16pt}
 149
 150  {\LARGE\bf
 151   Atomistic simulation studies\\[0.2cm]
 152   in the C/Si system
 153  }
 154
 155  \vspace{48pt}
 156
 157  \textsc{Frank Zirkelbach}
 158
 159  \vspace{48pt}
 160
 161  Application talk at the Max Planck Institute for Solid State Research
 162
 163  \vspace{08pt}
 164
 165  Stuttgart, November 2011
 166
 167 \end{center}
 168 \end{slide}
 169
 170 % no vertical centering
 171 \centerslidesfalse
 172
 173 \ifnum1=0
 174
 175 % intro
 176
 177 \begin{slide}
 178
 179 %{\large\bf
 180 % Phase diagram of the C/Si system\\
 181 %}
 182
 183 \vspace*{0.2cm}
 184
 185 \begin{minipage}{6.5cm}
 186 \includegraphics[width=6.5cm]{si-c_phase.eps}
 187 \begin{center}
 188 {\tiny
 189 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 190 }
 191 \end{center}
 192 \begin{pspicture}(0,0)(0,0)
 193 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 194 \end{pspicture}
 195 \end{minipage}
 196 \begin{minipage}{6cm}
 197 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 198 {\color{blue}Stoichiometric composition}
 199 \begin{itemize}
 200 \item only chemical stable compound
 201 \item wide band gap semiconductor\\
 202       \underline{silicon carbide}, SiC
 203 \end{itemize}
 204 \end{minipage}
 205
 206 \end{slide}
 207
 208 % motivation / properties / applications of silicon carbide
 209
 210 \begin{slide}
 211
 212 \vspace*{1.8cm}
 213
 214 \small
 215
 216 \begin{pspicture}(0,0)(13.5,5)
 217
 218  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
 219
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 222
 223  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 224
 225  \rput[lt](0.3,4){wide band gap}
 226  \rput[lt](0.3,3.5){high electric breakdown field}
 227  \rput[lt](0.3,3){good electron mobility}
 228  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 229  \rput[lt](0.3,2){high thermal conductivity}
 230
 231  \rput[lt](0.3,1.5){hard and mechanically stable}
 232  \rput[lt](0.3,1){chemically inert}
 233
 234  \rput[lt](0.3,0.5){radiation hardness}
 235
 236  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 237
 238  \rput[rt](12.5,3.85){high-temperature, high power}
 239  \rput[rt](12.5,3.5){and high-frequency}
 240  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 241
 242  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 243  \rput[rt](12.5,2){microelectromechanical systems}
 244  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 245
 246  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 247  \rput[rt](12.5,0.5){and electronic devices for space}
 248
 249 \end{pspicture}
 250
 251 \begin{picture}(0,0)(5,-162)
 252 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 253 \end{picture}
 254 \begin{picture}(0,0)(-120,-162)
 255 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 256 \end{picture}
 257 \begin{picture}(0,0)(-270,-162)
 258 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 259 \end{picture}
 260 %%%%
 261 \begin{picture}(0,0)(10,65)
 262 \includegraphics[height=2.8cm]{sic_switch.eps}
 263 \end{picture}
 264 %\begin{picture}(0,0)(-243,65)
 265 \begin{picture}(0,0)(-110,65)
 266 \includegraphics[height=2.8cm]{ise_99.eps}
 267 \end{picture}
 268 %\begin{picture}(0,0)(-135,65)
 269 \begin{picture}(0,0)(-100,65)
 270 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 271 \end{picture}
 272 \begin{picture}(0,0)(-233,65)
 273 \includegraphics[height=2.8cm]{solar_car.eps}
 274 \end{picture}
 275
 276 \end{slide}
 277
 278 % motivation
 279
 280 \begin{slide}
 281
 282  {\large\bf
 283   Polytypes of SiC\\[0.4cm]
 284  }
 285
 286 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 287 \begin{minipage}{1.9cm}
 288 {\tiny cubic (twist)}
 289 \end{minipage}
 290 \begin{minipage}{2.9cm}
 291 {\tiny hexagonal (no twist)}
 292 \end{minipage}
 293
 294 \begin{picture}(0,0)(-150,0)
 295  \includegraphics[width=7cm]{polytypes.eps}
 296 \end{picture}
 297
 298 \vspace{0.6cm}
 299
 300 \footnotesize
 301
 302 \begin{tabular}{l c c c c c c}
 303 \hline
 304  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 305 \hline
 306 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 307 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 308 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 309 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 310 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 311 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 312 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 313 \hline
 314 \end{tabular}
 315
 316 \begin{pspicture}(0,0)(0,0)
 317 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 318 \end{pspicture}
 319 \begin{pspicture}(0,0)(0,0)
 320 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 321 \end{pspicture}
 322 \begin{pspicture}(0,0)(0,0)
 323 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 324 \end{pspicture}
 325
 326 \end{slide}
 327
 328 % fabrication
 329
 330 \begin{slide}
 331
 332  {\large\bf
 333   Fabrication of silicon carbide
 334  }
 335
 336  \small
 337
 338  \vspace{2pt}
 339
 340 \begin{center}
 341  {\color{gray}
 342  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 343  }
 344 \end{center}
 345
 346 \vspace{2pt}
 347
 348 SiC thin films by MBE \& CVD
 349 \begin{itemize}
 350  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 351  \item \underline{Commercially available} semiconductor power devices based on
 352        \underline{\foreignlanguage{greek}{a}-SiC}
 353  \item Production of favored \underline{3C-SiC} material
 354        \underline{less advanced}
 355  \item Quality and size not yet sufficient
 356 \end{itemize}
 357 \begin{picture}(0,0)(-310,-20)
 358   \includegraphics[width=2.0cm]{cree.eps}
 359 \end{picture}
 360
 361 \vspace{-0.2cm}
 362
 363 Alternative approach:
 364 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 365
 366 \vspace{0.2cm}
 367
 368 \scriptsize
 369
 370 \framebox{
 371 \begin{minipage}{3.15cm}
 372  \begin{center}
 373 \includegraphics[width=3cm]{imp.eps}\\
 374  {\tiny
 375   Carbon implantation
 376  }
 377  \end{center}
 378 \end{minipage}
 379 \begin{minipage}{3.15cm}
 380  \begin{center}
 381 \includegraphics[width=3cm]{annealing.eps}\\
 382  {\tiny
 383   \unit[12]{h} annealing at \degc{1200}
 384  }
 385  \end{center}
 386 \end{minipage}
 387 }
 388 \begin{minipage}{5.5cm}
 389  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 390  \begin{center}
 391  {\tiny
 392   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 393  }
 394  \end{center}
 395 \end{minipage}
 396
 397 \end{slide}
 398
 399 % contents
 400
 401 \begin{slide}
 402
 403 {\large\bf
 404  Systematic investigation of C implantations into Si
 405 }
 406
 407 \vspace{1.7cm}
 408 \begin{center}
 409 \hspace{-1.0cm}
 410 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 411 \end{center}
 412
 413 \end{slide}
 414
 415 % outline
 416
 417 \begin{slide}
 418
 419 {\large\bf
 420  Outline
 421 }
 422
 423 \vspace{1.7cm}
 424 \begin{center}
 425 \hspace{-1.0cm}
 426 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 427 \end{center}
 428
 429 \begin{pspicture}(0,0)(0,0)
 430 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
 431 \begin{minipage}{11cm}
 432 {\color{black}Diploma thesis}\\
 433  \underline{Monte Carlo} simulation modeling the selforganization process\\
 434  leading to periodic arrays of nanometric amorphous SiC precipitates
 435 \end{minipage}
 436 }}}
 437 \end{pspicture}
 438 \begin{pspicture}(0,0)(0,0)
 439 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
 440 \begin{minipage}{11cm}
 441 {\color{black}Doctoral studies}\\
 442  Classical potential \underline{molecular dynamics} simulations \ldots\\
 443  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 444  \ldots on defect formation and SiC precipitation in Si
 445 \end{minipage}
 446 }}}
 447 \end{pspicture}
 448 \begin{pspicture}(0,0)(0,0)
 449 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 450 \end{pspicture}
 451 \begin{pspicture}(0,0)(0,0)
 452 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 453 \end{pspicture}
 454
 455 \end{slide}
 456
 457 \begin{slide}
 458
 459 \headdiplom
 460 {\large\bf
 461  Selforganization of nanometric amorphous SiC lamellae
 462 }
 463
 464 \small
 465
 466 \vspace{0.2cm}
 467
 468 \begin{itemize}
 469  \item Regularly spaced, nanometric spherical\\
 470        and lamellar amorphous inclusions\\
 471        at the upper a/c interface
 472  \item Carbon accumulation\\
 473        in amorphous volumes
 474 \end{itemize}
 475
 476 \vspace{0.4cm}
 477
 478 \begin{minipage}{12cm}
 479 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
 480 {\scriptsize
 481 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
 482 {\color{red}\underline{\degc{150}}},
 483 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
 484 }
 485 \end{minipage}
 486
 487 \begin{picture}(0,0)(-182,-215)
 488 \begin{minipage}{6.5cm}
 489 \begin{center}
 490 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
 491 {\scriptsize
 492 XTEM bright-field and respective EFTEM C map
 493 }
 494 \end{center}
 495 \end{minipage}
 496 \end{picture}
 497
 498 \end{slide}
 499
 500 \begin{slide}
 501
 502 \headdiplom
 503 {\large\bf
 504  Model displaying the formation of ordered lamellae
 505 }
 506
 507 \vspace{0.1cm}
 508
 509 \begin{center}
 510  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
 511 \end{center}
 512
 513 \footnotesize
 514
 515 \begin{itemize}
 516 \item Supersaturation of C in c-Si\\
 517       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
 518       SiC$_x$-precipitates
 519 \item High interfacial energy between 3C-SiC and c-Si\\
 520       $\rightarrow$ {\bf Amorphous} precipitates
 521 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
 522       $\rightarrow$ {\bf Lateral strain} (black arrows)
 523 \item Implantation range near surface\\
 524       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 525 \item Reduction of the carbon supersaturation in c-Si\\
 526       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
 527       (white arrows)
 528 \item Remaining lateral strain\\
 529       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
 530 \item Absence of crystalline neighbours (structural information)\\
 531       $\rightarrow$ {\bf Stabilization} of amorphous inclusions
 532       {\bf against recrystallization}
 533 \end{itemize}
 534
 535 \end{slide}
 536
 537 \begin{slide}
 538
 539 \headdiplom
 540 {\large\bf
 541  Implementation of the Monte Carlo code
 542 }
 543
 544 \small
 545
 546 \begin{enumerate}
 547  \item \underline{Amorphization / Recrystallization}\\
 548        Ion collision in discretized target determined by random numbers
 549        distributed according to nuclear energy loss.
 550        Amorphization/recrystallization probability:
 551 \[
 552 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 553 \]
 554 \begin{itemize}
 555  \item {\color{green} $p_b$} normal `ballistic' amorphization
 556  \item {\color{blue} $p_c$} carbon induced amorphization
 557  \item {\color{red} $p_s$} stress enhanced amorphization
 558 \end{itemize}
 559 \[
 560 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 561 \]
 562 \[
 563 \delta (\vec r) = \left\{
 564 \begin{array}{ll}
 565         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 566         0 & \textrm{otherwise} \\
 567 \end{array}
 568 \right.
 569 \]
 570  \item \underline{Carbon incorporation}\\
 571        Incorporation volume determined according to implantation profile
 572  \item \underline{Diffusion / Sputtering}
 573        \begin{itemize}
 574         \item Transfer fraction of C atoms
 575               of crystalline into neighbored amorphous volumes
 576         \item Remove surface layer
 577        \end{itemize}
 578 \end{enumerate}
 579
 580 \end{slide}
 581
 582 \begin{slide}
 583
 584 \begin{minipage}{3.7cm}
 585 \begin{pspicture}(0,0)(0,0)
 586 \rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
 587 \begin{minipage}{3.7cm}
 588 \hfill
 589 \vspace{0.7cm}
 590 \end{minipage}
 591 }}
 592 \end{pspicture}
 593 {\large\bf
 594  Results
 595 }
 596
 597 \footnotesize
 598
 599 \vspace{1.2cm}
 600
 601 Evolution of the \ldots
 602 \begin{itemize}
 603  \item continuous\\
 604        amorphous layer
 605  \item a/c interface
 606  \item lamellar precipitates
 607 \end{itemize}
 608 \ldots reproduced!\\[1.4cm]
 609
 610 {\color{blue}
 611 \begin{center}
 612 Experiment \& simulation\\
 613 in good agreement\\[1.0cm]
 614
 615 Simulation is able to model the whole depth region\\[1.2cm]
 616 \end{center}
 617 }
 618
 619 \end{minipage}
 620 \begin{minipage}{0.5cm}
 621 \vfill
 622 \end{minipage}
 623 \begin{minipage}{8.0cm}
 624  \vspace{-0.3cm}
 625  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
 626  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
 627 \end{minipage}
 628
 629 \end{slide}
 630
 631 \begin{slide}
 632
 633 \headdiplom
 634 {\large\bf
 635  Structural \& compositional details
 636 }
 637
 638 \begin{minipage}[t]{7.5cm}
 639 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
 640 \end{minipage}
 641 \begin{minipage}[t]{5.0cm}
 642 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
 643 \end{minipage}
 644
 645 \footnotesize
 646
 647 \vspace{-0.1cm}
 648
 649 \begin{itemize}
 650  \item Fluctuation of C concentration in lamellae region
 651  \item \unit[8--10]{at.\%} C saturation limit
 652        within the respective conditions
 653  \item Complementarily arranged and alternating sequence of layers\\
 654        with a high and low amount of amorphous regions
 655  \item C accumulation in the amorphous phase / Origin of stress
 656 \end{itemize}
 657
 658 \begin{picture}(0,0)(-260,-50)
 659 \framebox{
 660 \begin{minipage}{3cm}
 661 \begin{center}
 662 {\color{blue}
 663 Precipitation process\\
 664 gets traceable\\
 665 by simulation!
 666 }
 667 \end{center}
 668 \end{minipage}
 669 }
 670 \end{picture}
 671
 672 \end{slide}
 673
 674 \begin{slide}
 675
 676 \headphd
 677 {\large\bf
 678  Formation of epitaxial single crystalline 3C-SiC
 679 }
 680
 681 \footnotesize
 682
 683 \vspace{0.2cm}
 684
 685 \begin{center}
 686 \begin{itemize}
 687  \item \underline{Implantation step 1}\\[0.1cm]
 688         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
 689         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
 690         {\color{blue}precipitates}
 691  \item \underline{Implantation step 2}\\[0.1cm]
 692         Little remaining dose | \unit[180]{keV} | \degc{250}\\
 693         $\Rightarrow$
 694         Destruction/Amorphization of precipitates at layer interface
 695  \item \underline{Annealing}\\[0.1cm]
 696        \unit[10]{h} at \degc{1250}\\
 697        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
 698 \end{itemize}
 699 \end{center}
 700
 701 \begin{minipage}{7cm}
 702 \includegraphics[width=7cm]{ibs_3c-sic.eps}
 703 \end{minipage}
 704 \begin{minipage}{5cm}
 705 \begin{pspicture}(0,0)(0,0)
 706 \rnode{box}{
 707 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
 708 \begin{minipage}{5.3cm}
 709  \begin{center}
 710  {\color{blue}
 711   3C-SiC precipitation\\
 712   not yet fully understood
 713  }
 714  \end{center}
 715  \vspace*{0.1cm}
 716  \renewcommand\labelitemi{$\Rightarrow$}
 717  Details of the SiC precipitation
 718  \begin{itemize}
 719   \item significant technological progress\\
 720         in SiC thin film formation
 721   \item perspectives for processes relying\\
 722         upon prevention of SiC precipitation
 723  \end{itemize}
 724 \end{minipage}
 725 }}
 726 \rput(-6.8,5.4){\pnode{h0}}
 727 \rput(-3.0,5.4){\pnode{h1}}
 728 \ncline[linecolor=blue]{-}{h0}{h1}
 729 \ncline[linecolor=blue]{->}{h1}{box}
 730 \end{pspicture}
 731 \end{minipage}
 732
 733 \end{slide}
 734
 735 \begin{slide}
 736
 737 \headphd
 738 {\large\bf
 739   Supposed precipitation mechanism of SiC in Si
 740 }
 741
 742  \scriptsize
 743
 744  \vspace{0.1cm}
 745
 746  \framebox{
 747  \begin{minipage}{3.6cm}
 748  \begin{center}
 749  Si \& SiC lattice structure\\[0.1cm]
 750  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 751  \end{center}
 752 {\tiny
 753  \begin{minipage}{1.7cm}
 754 \underline{Silicon}\\
 755 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 756 $a=\unit[5.429]{\\A}$\\
 757 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 758  \end{minipage}
 759  \begin{minipage}{1.7cm}
 760 \underline{Silicon carbide}\\
 761 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 762 $a=\unit[4.359]{\\A}$\\
 763 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 764  \end{minipage}
 765 }
 766  \end{minipage}
 767  }
 768  \hspace{0.1cm}
 769  \begin{minipage}{4.1cm}
 770  \begin{center}
 771  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 772  \end{center}
 773  \end{minipage}
 774  \hspace{0.1cm}
 775  \begin{minipage}{4.0cm}
 776  \begin{center}
 777  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 778  \end{center}
 779  \end{minipage}
 780
 781  \vspace{0.1cm}
 782
 783  \begin{minipage}{4.0cm}
 784  \begin{center}
 785  C-Si dimers (dumbbells)\\[-0.1cm]
 786  on Si interstitial sites
 787  \end{center}
 788  \end{minipage}
 789  \hspace{0.1cm}
 790  \begin{minipage}{4.1cm}
 791  \begin{center}
 792  Agglomeration of C-Si dumbbells\\[-0.1cm]
 793  $\Rightarrow$ dark contrasts
 794  \end{center}
 795  \end{minipage}
 796  \hspace{0.1cm}
 797  \begin{minipage}{4.0cm}
 798  \begin{center}
 799  Precipitation of 3C-SiC in Si\\[-0.1cm]
 800  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 801  \& release of Si self-interstitials
 802  \end{center}
 803  \end{minipage}
 804
 805  \vspace{0.1cm}
 806
 807  \begin{minipage}{4.0cm}
 808  \begin{center}
 809  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 810  \end{center}
 811  \end{minipage}
 812  \hspace{0.1cm}
 813  \begin{minipage}{4.1cm}
 814  \begin{center}
 815  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 816  \end{center}
 817  \end{minipage}
 818  \hspace{0.1cm}
 819  \begin{minipage}{4.0cm}
 820  \begin{center}
 821  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 822  \end{center}
 823  \end{minipage}
 824
 825 \begin{pspicture}(0,0)(0,0)
 826 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 827 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 828 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 829 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 830 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 831  $4a_{\text{Si}}=5a_{\text{SiC}}$
 832  }}}
 833 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 834 \hkl(h k l) planes match
 835  }}}
 836 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 837 r = \unit[2--4]{nm}
 838  }}}
 839 \end{pspicture}
 840
 841 \end{slide}
 842
 843 \begin{slide}
 844
 845 \headphd
 846 {\large\bf
 847  Supposed precipitation mechanism of SiC in Si
 848 }
 849
 850  \scriptsize
 851
 852  \vspace{0.1cm}
 853
 854  \framebox{
 855  \begin{minipage}{3.6cm}
 856  \begin{center}
 857  Si \& SiC lattice structure\\[0.1cm]
 858  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 859  \end{center}
 860 {\tiny
 861  \begin{minipage}{1.7cm}
 862 \underline{Silicon}\\
 863 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 864 $a=\unit[5.429]{\\A}$\\
 865 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 866  \end{minipage}
 867  \begin{minipage}{1.7cm}
 868 \underline{Silicon carbide}\\
 869 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 870 $a=\unit[4.359]{\\A}$\\
 871 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 872  \end{minipage}
 873 }
 874  \end{minipage}
 875  }
 876  \hspace{0.1cm}
 877  \begin{minipage}{4.1cm}
 878  \begin{center}
 879  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 880  \end{center}
 881  \end{minipage}
 882  \hspace{0.1cm}
 883  \begin{minipage}{4.0cm}
 884  \begin{center}
 885  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 886  \end{center}
 887  \end{minipage}
 888
 889  \vspace{0.1cm}
 890
 891  \begin{minipage}{4.0cm}
 892  \begin{center}
 893  C-Si dimers (dumbbells)\\[-0.1cm]
 894  on Si interstitial sites
 895  \end{center}
 896  \end{minipage}
 897  \hspace{0.1cm}
 898  \begin{minipage}{4.1cm}
 899  \begin{center}
 900  Agglomeration of C-Si dumbbells\\[-0.1cm]
 901  $\Rightarrow$ dark contrasts
 902  \end{center}
 903  \end{minipage}
 904  \hspace{0.1cm}
 905  \begin{minipage}{4.0cm}
 906  \begin{center}
 907  Precipitation of 3C-SiC in Si\\[-0.1cm]
 908  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 909  \& release of Si self-interstitials
 910  \end{center}
 911  \end{minipage}
 912
 913  \vspace{0.1cm}
 914
 915  \begin{minipage}{4.0cm}
 916  \begin{center}
 917  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 918  \end{center}
 919  \end{minipage}
 920  \hspace{0.1cm}
 921  \begin{minipage}{4.1cm}
 922  \begin{center}
 923  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 924  \end{center}
 925  \end{minipage}
 926  \hspace{0.1cm}
 927  \begin{minipage}{4.0cm}
 928  \begin{center}
 929  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 930  \end{center}
 931  \end{minipage}
 932
 933 \begin{pspicture}(0,0)(0,0)
 934 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 935 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 936 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 937 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 938 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 939  $4a_{\text{Si}}=5a_{\text{SiC}}$
 940  }}}
 941 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 942 \hkl(h k l) planes match
 943  }}}
 944 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 945 r = \unit[2--4]{nm}
 946  }}}
 947 % controversial view!
 948 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
 949 \begin{minipage}{14cm}
 950 \hfill
 951 \vspace{12cm}
 952 \end{minipage}
 953 }}
 954 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
 955 \begin{minipage}{10cm}
 956 \small
 957 \vspace*{0.2cm}
 958 \begin{center}
 959 {\color{gray}\bf Controversial findings}
 960 \end{center}
 961 \begin{itemize}
 962 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
 963  \begin{itemize}
 964   \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
 965   \item \si{} reacting with further C in cleared volume
 966  \end{itemize}
 967 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
 968  \begin{itemize}
 969   \item Room temperature implantation $\rightarrow$ high C diffusion
 970   \item Elevated temperature implantation $\rightarrow$ no C redistribution
 971  \end{itemize}
 972  $\Rightarrow$ mobile {\color{red}\ci} opposed to
 973  stable {\color{blue}\cs{}} configurations
 974 \item Strained silicon \& Si/SiC heterostructures
 975       {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
 976  \begin{itemize}
 977   \item {\color{blue}Coherent} SiC precipitates (tensile strain)
 978   \item Incoherent SiC (strain relaxation)
 979  \end{itemize}
 980 \end{itemize}
 981 \vspace{0.1cm}
 982 \begin{center}
 983 {\Huge${\lightning}$} \hspace{0.3cm}
 984 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
 985 {\Huge${\lightning}$}
 986 \end{center}
 987 \vspace{0.2cm}
 988 \end{minipage}
 989  }}}
 990 \end{pspicture}
 991
 992 \end{slide}
 993
 994 % continue here
 995 \fi
 996
 997 \begin{slide}
 998
 999 \headphd
1000 {\large\bf
1001  Utilized computational methods
1002 }
1003
1004 \vspace{0.2cm}
1005
1006 \small
1007
1008 {\bf Molecular dynamics (MD)}\\
1009 \scriptsize
1010 \begin{tabular}{p{4.5cm} p{7.5cm}}
1011 Basics & Details\\
1012 \hline
1013 System of $N$ particles &
1014 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
1015 \hline
1016 Phase space propagation &
1017 Velocity Verlet | timestep: \unit[1]{fs} \\
1018 \hline
1019 Analytical interaction potential &
1020 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
1021 (Erhart/Albe)
1022 $\displaystyle
1023 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1024     \pot_{ij} = {\color{red}f_C(r_{ij})}
1025     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1026 $\\
1027 \hline
1028 Observables: time/ensemble averages &
1029 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
1030 \hline
1031 \end{tabular}
1032
1033 \small
1034
1035 \vspace{0.1cm}
1036
1037 {\bf Density functional theory (DFT)}
1038
1039 \scriptsize
1040
1041 \begin{minipage}[t]{6cm}
1042 \underline{Basics}
1043 \begin{itemize}
1044  \item $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
1045  \item Single-particle effective theory
1046 % \item Born-Oppenheimer approximation:\\
1047 %       Decouple electronic \& ionic motion
1048 % \item Hohenberg-Kohn theorem:\\
1049 %       $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
1050 %       $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
1051 \end{itemize}
1052 \underline{Details}
1053 \begin{itemize}
1054 \item Code: \textsc{vasp}
1055 \item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
1056 $\displaystyle
1057 \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
1058 $\\
1059 $\displaystyle
1060 E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
1061 $
1062 \item Ultrasoft pseudopotential
1063 \item Exchange \& correlation: GGA
1064 \item Brillouin zone sampling: $\Gamma$-point
1065 \end{itemize}
1066 \end{minipage}
1067 \begin{minipage}[t]{6cm}
1068
1069 \[
1070 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
1071 \]
1072 \[
1073 n(r)=\sum_i^N|\Phi_i(r)|^2
1074 \]
1075 \[
1076 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1077                  +V_{\text{XC}}[n(r)]
1078 \]
1079
1080 \end{minipage}
1081
1082 \end{slide}
1083
1084 \end{document}
1085 \ifnum1=0
1086
1087 \begin{slide}
1088
1089  \small
1090  {\large\bf
1091   Density functional theory (DFT) calculations
1092  }
1093
1094  Basic ingredients necessary for DFT
1095
1096  \begin{itemize}
1097   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1098         \begin{itemize}
1099          \item ... uniquely determines the ground state potential
1100                / wavefunctions
1101          \item ... minimizes the systems total energy
1102         \end{itemize}
1103   \item \underline{Born-Oppenheimer}
1104         - $N$ moving electrons in an external potential of static nuclei
1105 \[
1106 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1107               +\sum_i^N V_{\text{ext}}(r_i)
1108               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1109 \]
1110   \item \underline{Effective potential}
1111         - averaged electrostatic potential \& exchange and correlation
1112 \[
1113 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1114                  +V_{\text{XC}}[n(r)]
1115 \]
1116   \item \underline{Kohn-Sham system}
1117         - Schr\"odinger equation of N non-interacting particles
1118 \[
1119 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1120 =\epsilon_i\Phi_i(r)
1121 \quad
1122 \Rightarrow
1123 \quad
1124 n(r)=\sum_i^N|\Phi_i(r)|^2
1125 \]
1126   \item \underline{Self-consistent solution}\\
1127 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1128 which in turn depends on $n(r)$
1129   \item \underline{Variational principle}
1130         - minimize total energy with respect to $n(r)$
1131  \end{itemize}
1132
1133 \end{slide}
1134
1135 \begin{slide}
1136
1137  {\large\bf
1138   Density functional theory (DFT) calculations
1139  }
1140
1141  \small
1142
1143  \vspace*{0.2cm}
1144
1145  Details of applied DFT calculations in this work
1146
1147  \begin{itemize}
1148   \item \underline{Exchange correlation functional}
1149         - approximations for the inhomogeneous electron gas
1150         \begin{itemize}
1151          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1152          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1153         \end{itemize}
1154   \item \underline{Plane wave basis set}
1155         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1156   \item \underline{Brillouin zone sampling} -
1157         {\color{blue}$\Gamma$-point only} calculations
1158   \item \underline{Pseudo potential}
1159         - consider only the valence electrons
1160   \item \underline{Code} - VASP 4.6
1161  \end{itemize}
1162
1163  \vspace*{0.2cm}
1164
1165  MD and structural optimization
1166
1167  \begin{itemize}
1168   \item MD integration: Gear predictor corrector algorithm
1169   \item Pressure control: Parrinello-Rahman pressure control
1170   \item Structural optimization: Conjugate gradient method
1171  \end{itemize}
1172
1173 \begin{pspicture}(0,0)(0,0)
1174 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1175 \end{pspicture}
1176
1177 \end{slide}
1178
1179 \begin{slide}
1180
1181  {\large\bf
1182   C and Si self-interstitial point defects in silicon
1183  }
1184
1185  \small
1186
1187  \vspace*{0.3cm}
1188
1189 \begin{minipage}{8cm}
1190 Procedure:\\[0.3cm]
1191   \begin{pspicture}(0,0)(7,5)
1192   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1193    \parbox{7cm}{
1194    \begin{itemize}
1195     \item Creation of c-Si simulation volume
1196     \item Periodic boundary conditions
1197     \item $T=0\text{ K}$, $p=0\text{ bar}$
1198    \end{itemize}
1199   }}}}
1200 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1201  \parbox{7cm}{
1202   \begin{center}
1203   Insertion of interstitial C/Si atoms
1204   \end{center}
1205   }}}}
1206   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1207    \parbox{7cm}{
1208    \begin{center}
1209    Relaxation / structural energy minimization
1210    \end{center}
1211   }}}}
1212   \ncline[]{->}{init}{insert}
1213   \ncline[]{->}{insert}{cool}
1214  \end{pspicture}
1215 \end{minipage}
1216 \begin{minipage}{5cm}
1217   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1218 \end{minipage}
1219
1220 \begin{minipage}{9cm}
1221  \begin{tabular}{l c c}
1222  \hline
1223  & size [unit cells] & \# atoms\\
1224 \hline
1225 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1226 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1227 \hline
1228  \end{tabular}
1229 \end{minipage}
1230 \begin{minipage}{4cm}
1231 {\color{red}$\bullet$} Tetrahedral\\
1232 {\color{green}$\bullet$} Hexagonal\\
1233 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1234 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1235 {\color{cyan}$\bullet$} Bond-centered\\
1236 {\color{black}$\bullet$} Vacancy / Substitutional
1237 \end{minipage}
1238
1239 \end{slide}
1240
1241 \begin{slide}
1242
1243  \footnotesize
1244
1245 \begin{minipage}{9.5cm}
1246
1247  {\large\bf
1248   Si self-interstitial point defects in silicon\\
1249  }
1250
1251 \begin{tabular}{l c c c c c}
1252 \hline
1253  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1254 \hline
1255  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1256  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1257 \hline
1258 \end{tabular}\\[0.2cm]
1259
1260 \begin{minipage}{4.7cm}
1261 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1262 \end{minipage}
1263 \begin{minipage}{4.7cm}
1264 \begin{center}
1265 {\tiny nearly T $\rightarrow$ T}\\
1266 \end{center}
1267 \includegraphics[width=4.7cm]{nhex_tet.ps}
1268 \end{minipage}\\
1269
1270 \underline{Hexagonal} \hspace{2pt}
1271 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1272 \framebox{
1273 \begin{minipage}{2.7cm}
1274 $E_{\text{f}}^*=4.48\text{ eV}$\\
1275 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1276 \end{minipage}
1277 \begin{minipage}{0.4cm}
1278 \begin{center}
1279 $\Rightarrow$
1280 \end{center}
1281 \end{minipage}
1282 \begin{minipage}{2.7cm}
1283 $E_{\text{f}}=3.96\text{ eV}$\\
1284 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1285 \end{minipage}
1286 }
1287 \begin{minipage}{2.9cm}
1288 \begin{flushright}
1289 \underline{Vacancy}\\
1290 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1291 \end{flushright}
1292 \end{minipage}
1293
1294 \end{minipage}
1295 \begin{minipage}{3.5cm}
1296
1297 \begin{flushright}
1298 \underline{\hkl<1 1 0> dumbbell}\\
1299 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1300 \underline{Tetrahedral}\\
1301 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1302 \underline{\hkl<1 0 0> dumbbell}\\
1303 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1304 \end{flushright}
1305
1306 \end{minipage}
1307
1308 \end{slide}
1309
1310 \begin{slide}
1311
1312 \footnotesize
1313
1314  {\large\bf
1315   C interstitial point defects in silicon\\[-0.1cm]
1316  }
1317
1318 \begin{tabular}{l c c c c c c r}
1319 \hline
1320  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1321 \hline
1322  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1323  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1324 \hline
1325 \end{tabular}\\[0.1cm]
1326
1327 \framebox{
1328 \begin{minipage}{2.7cm}
1329 \underline{Hexagonal} \hspace{2pt}
1330 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1331 $E_{\text{f}}^*=9.05\text{ eV}$\\
1332 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1333 \end{minipage}
1334 \begin{minipage}{0.4cm}
1335 \begin{center}
1336 $\Rightarrow$
1337 \end{center}
1338 \end{minipage}
1339 \begin{minipage}{2.7cm}
1340 \underline{\hkl<1 0 0>}\\
1341 $E_{\text{f}}=3.88\text{ eV}$\\
1342 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1343 \end{minipage}
1344 }
1345 \begin{minipage}{2cm}
1346 \hfill
1347 \end{minipage}
1348 \begin{minipage}{3cm}
1349 \begin{flushright}
1350 \underline{Tetrahedral}\\
1351 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1352 \end{flushright}
1353 \end{minipage}
1354
1355 \framebox{
1356 \begin{minipage}{2.7cm}
1357 \underline{Bond-centered}\\
1358 $E_{\text{f}}^*=5.59\text{ eV}$\\
1359 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1360 \end{minipage}
1361 \begin{minipage}{0.4cm}
1362 \begin{center}
1363 $\Rightarrow$
1364 \end{center}
1365 \end{minipage}
1366 \begin{minipage}{2.7cm}
1367 \underline{\hkl<1 1 0> dumbbell}\\
1368 $E_{\text{f}}=5.18\text{ eV}$\\
1369 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1370 \end{minipage}
1371 }
1372 \begin{minipage}{2cm}
1373 \hfill
1374 \end{minipage}
1375 \begin{minipage}{3cm}
1376 \begin{flushright}
1377 \underline{Substitutional}\\
1378 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1379 \end{flushright}
1380 \end{minipage}
1381
1382 \end{slide}
1383
1384 \begin{slide}
1385
1386 \footnotesize
1387
1388  {\large\bf\boldmath
1389   C \hkl<1 0 0> dumbbell interstitial configuration\\
1390  }
1391
1392 {\tiny
1393 \begin{tabular}{l c c c c c c c c}
1394 \hline
1395  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1396 \hline
1397 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1398 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1399 \hline
1400 \end{tabular}\\[0.2cm]
1401 \begin{tabular}{l c c c c }
1402 \hline
1403  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1404 \hline
1405 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1406 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1407 \hline
1408 \end{tabular}\\[0.2cm]
1409 \begin{tabular}{l c c c}
1410 \hline
1411  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1412 \hline
1413 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1414 VASP & 0.109 & -0.065 & 0.174 \\
1415 \hline
1416 \end{tabular}\\[0.6cm]
1417 }
1418
1419 \begin{minipage}{3.0cm}
1420 \begin{center}
1421 \underline{Erhart/Albe}
1422 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1423 \end{center}
1424 \end{minipage}
1425 \begin{minipage}{3.0cm}
1426 \begin{center}
1427 \underline{VASP}
1428 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1429 \end{center}
1430 \end{minipage}\\
1431
1432 \begin{picture}(0,0)(-185,10)
1433 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1434 \end{picture}
1435 \begin{picture}(0,0)(-280,-150)
1436 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1437 \end{picture}
1438
1439 \begin{pspicture}(0,0)(0,0)
1440 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1441 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1442 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1443 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1444 \end{pspicture}
1445
1446 \end{slide}
1447
1448 \begin{slide}
1449
1450 \small
1451
1452 \begin{minipage}{8.5cm}
1453
1454  {\large\bf
1455   Bond-centered interstitial configuration\\[-0.1cm]
1456  }
1457
1458 \begin{minipage}{3.0cm}
1459 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1460 \end{minipage}
1461 \begin{minipage}{5.2cm}
1462 \begin{itemize}
1463  \item Linear Si-C-Si bond
1464  \item Si: one C \& 3 Si neighbours
1465  \item Spin polarized calculations
1466  \item No saddle point!\\
1467        Real local minimum!
1468 \end{itemize}
1469 \end{minipage}
1470
1471 \framebox{
1472  \tiny
1473  \begin{minipage}[t]{6.5cm}
1474   \begin{minipage}[t]{1.2cm}
1475   {\color{red}Si}\\
1476   {\tiny sp$^3$}\\[0.8cm]
1477   \underline{${\color{black}\uparrow}$}
1478   \underline{${\color{black}\uparrow}$}
1479   \underline{${\color{black}\uparrow}$}
1480   \underline{${\color{red}\uparrow}$}\\
1481   sp$^3$
1482   \end{minipage}
1483   \begin{minipage}[t]{1.4cm}
1484   \begin{center}
1485   {\color{red}M}{\color{blue}O}\\[0.8cm]
1486   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1487   $\sigma_{\text{ab}}$\\[0.5cm]
1488   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1489   $\sigma_{\text{b}}$
1490   \end{center}
1491   \end{minipage}
1492   \begin{minipage}[t]{1.0cm}
1493   \begin{center}
1494   {\color{blue}C}\\
1495   {\tiny sp}\\[0.2cm]
1496   \underline{${\color{white}\uparrow\uparrow}$}
1497   \underline{${\color{white}\uparrow\uparrow}$}\\
1498   2p\\[0.4cm]
1499   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1500   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1501   sp
1502   \end{center}
1503   \end{minipage}
1504   \begin{minipage}[t]{1.4cm}
1505   \begin{center}
1506   {\color{blue}M}{\color{green}O}\\[0.8cm]
1507   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1508   $\sigma_{\text{ab}}$\\[0.5cm]
1509   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1510   $\sigma_{\text{b}}$
1511   \end{center}
1512   \end{minipage}
1513   \begin{minipage}[t]{1.2cm}
1514   \begin{flushright}
1515   {\color{green}Si}\\
1516   {\tiny sp$^3$}\\[0.8cm]
1517   \underline{${\color{green}\uparrow}$}
1518   \underline{${\color{black}\uparrow}$}
1519   \underline{${\color{black}\uparrow}$}
1520   \underline{${\color{black}\uparrow}$}\\
1521   sp$^3$
1522   \end{flushright}
1523   \end{minipage}
1524  \end{minipage}
1525 }\\[0.1cm]
1526
1527 \framebox{
1528 \begin{minipage}{4.5cm}
1529 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1530 \end{minipage}
1531 \begin{minipage}{3.5cm}
1532 {\color{gray}$\bullet$} Spin up\\
1533 {\color{green}$\bullet$} Spin down\\
1534 {\color{blue}$\bullet$} Resulting spin up\\
1535 {\color{yellow}$\bullet$} Si atoms\\
1536 {\color{red}$\bullet$} C atom
1537 \end{minipage}
1538 }
1539
1540 \end{minipage}
1541 \begin{minipage}{4.2cm}
1542 \begin{flushright}
1543 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1544 {\color{green}$\Box$} {\tiny unoccupied}\\
1545 {\color{red}$\bullet$} {\tiny occupied}
1546 \end{flushright}
1547 \end{minipage}
1548
1549 \end{slide}
1550
1551 \begin{slide}
1552
1553  {\large\bf\boldmath
1554   Migration of the C \hkl<1 0 0> dumbbell interstitial
1555  }
1556
1557 \scriptsize
1558
1559  {\small Investigated pathways}
1560
1561 \begin{minipage}{8.5cm}
1562 \begin{minipage}{8.3cm}
1563 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1564 \begin{minipage}{2.4cm}
1565 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1566 \end{minipage}
1567 \begin{minipage}{0.4cm}
1568 $\rightarrow$
1569 \end{minipage}
1570 \begin{minipage}{2.4cm}
1571 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1572 \end{minipage}
1573 \begin{minipage}{0.4cm}
1574 $\rightarrow$
1575 \end{minipage}
1576 \begin{minipage}{2.4cm}
1577 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1578 \end{minipage}
1579 \end{minipage}\\
1580 \begin{minipage}{8.3cm}
1581 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1582 \begin{minipage}{2.4cm}
1583 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1584 \end{minipage}
1585 \begin{minipage}{0.4cm}
1586 $\rightarrow$
1587 \end{minipage}
1588 \begin{minipage}{2.4cm}
1589 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1590 \end{minipage}
1591 \begin{minipage}{0.4cm}
1592 $\rightarrow$
1593 \end{minipage}
1594 \begin{minipage}{2.4cm}
1595 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1596 \end{minipage}
1597 \end{minipage}\\
1598 \begin{minipage}{8.3cm}
1599 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1600 \begin{minipage}{2.4cm}
1601 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1602 \end{minipage}
1603 \begin{minipage}{0.4cm}
1604 $\rightarrow$
1605 \end{minipage}
1606 \begin{minipage}{2.4cm}
1607 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1608 \end{minipage}
1609 \begin{minipage}{0.4cm}
1610 $\rightarrow$
1611 \end{minipage}
1612 \begin{minipage}{2.4cm}
1613 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1614 \end{minipage}
1615 \end{minipage}
1616 \end{minipage}
1617 \framebox{
1618 \begin{minipage}{4.2cm}
1619  {\small Constrained relaxation\\
1620          technique (CRT) method}\\
1621 \includegraphics[width=4cm]{crt_orig.eps}
1622 \begin{itemize}
1623  \item Constrain diffusing atom
1624  \item Static constraints
1625 \end{itemize}
1626 \vspace*{0.3cm}
1627  {\small Modifications}\\
1628 \includegraphics[width=4cm]{crt_mod.eps}
1629 \begin{itemize}
1630  \item Constrain all atoms
1631  \item Update individual\\
1632        constraints
1633 \end{itemize}
1634 \end{minipage}
1635 }
1636
1637 \end{slide}
1638
1639 \begin{slide}
1640
1641  {\large\bf\boldmath
1642   Migration of the C \hkl<1 0 0> dumbbell interstitial
1643  }
1644
1645 \scriptsize
1646
1647 \framebox{
1648 \begin{minipage}{5.9cm}
1649 \begin{flushleft}
1650 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1651 \end{flushleft}
1652 \begin{center}
1653 \begin{picture}(0,0)(60,0)
1654 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1655 \end{picture}
1656 \begin{picture}(0,0)(-5,0)
1657 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1658 \end{picture}
1659 \begin{picture}(0,0)(-55,0)
1660 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1661 \end{picture}
1662 \begin{picture}(0,0)(12.5,10)
1663 \includegraphics[width=1cm]{110_arrow.eps}
1664 \end{picture}
1665 \begin{picture}(0,0)(90,0)
1666 \includegraphics[height=0.9cm]{001_arrow.eps}
1667 \end{picture}
1668 \end{center}
1669 \vspace*{0.35cm}
1670 \end{minipage}
1671 }
1672 \begin{minipage}{0.3cm}
1673 \hfill
1674 \end{minipage}
1675 \framebox{
1676 \begin{minipage}{5.9cm}
1677 \begin{flushright}
1678 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1679 \end{flushright}
1680 \begin{center}
1681 \begin{picture}(0,0)(60,0)
1682 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1683 \end{picture}
1684 \begin{picture}(0,0)(5,0)
1685 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1686 \end{picture}
1687 \begin{picture}(0,0)(-55,0)
1688 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1689 \end{picture}
1690 \begin{picture}(0,0)(12.5,10)
1691 \includegraphics[width=1cm]{100_arrow.eps}
1692 \end{picture}
1693 \begin{picture}(0,0)(90,0)
1694 \includegraphics[height=0.9cm]{001_arrow.eps}
1695 \end{picture}
1696 \end{center}
1697 \vspace*{0.3cm}
1698 \end{minipage}\\
1699 }
1700
1701 \vspace*{0.05cm}
1702
1703 \framebox{
1704 \begin{minipage}{5.9cm}
1705 \begin{flushleft}
1706 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1707 \end{flushleft}
1708 \begin{center}
1709 \begin{picture}(0,0)(60,0)
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1711 \end{picture}
1712 \begin{picture}(0,0)(10,0)
1713 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1714 \end{picture}
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1720 \end{picture}
1721 \begin{picture}(0,0)(90,0)
1722 \includegraphics[height=0.9cm]{001_arrow.eps}
1723 \end{picture}
1724 \end{center}
1725 \vspace*{0.3cm}
1726 \end{minipage}
1727 }
1728 \begin{minipage}{0.3cm}
1729 \hfill
1730 \end{minipage}
1731 \begin{minipage}{6.5cm}
1732 VASP results
1733 \begin{itemize}
1734  \item Energetically most favorable path
1735        \begin{itemize}
1736         \item Path 2
1737         \item Activation energy: $\approx$ 0.9 eV
1738         \item Experimental values: 0.73 ... 0.87 eV
1739        \end{itemize}
1740        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1741  \item Reorientation (path 3)
1742        \begin{itemize}
1743         \item More likely composed of two consecutive steps of type 2
1744         \item Experimental values: 0.77 ... 0.88 eV
1745        \end{itemize}
1746        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1747 \end{itemize}
1748 \end{minipage}
1749
1750 \end{slide}
1751
1752 \begin{slide}
1753
1754  {\large\bf\boldmath
1755   Migration of the C \hkl<1 0 0> dumbbell interstitial
1756  }
1757
1758 \scriptsize
1759
1760  \vspace{0.1cm}
1761
1762 \begin{minipage}{6.5cm}
1763
1764 \framebox{
1765 \begin{minipage}[t]{5.9cm}
1766 \begin{flushleft}
1767 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1768 \end{flushleft}
1769 \begin{center}
1770 \begin{pspicture}(0,0)(0,0)
1771 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1772 \end{pspicture}
1773 \begin{picture}(0,0)(60,-50)
1774 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1775 \end{picture}
1776 \begin{picture}(0,0)(5,-50)
1777 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1778 \end{picture}
1779 \begin{picture}(0,0)(-55,-50)
1780 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1781 \end{picture}
1782 \begin{picture}(0,0)(12.5,-40)
1783 \includegraphics[width=1cm]{110_arrow.eps}
1784 \end{picture}
1785 \begin{picture}(0,0)(90,-45)
1786 \includegraphics[height=0.9cm]{001_arrow.eps}
1787 \end{picture}\\
1788 \begin{pspicture}(0,0)(0,0)
1789 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1790 \end{pspicture}
1791 \begin{picture}(0,0)(60,-15)
1792 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1793 \end{picture}
1794 \begin{picture}(0,0)(35,-15)
1795 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1796 \end{picture}
1797 \begin{picture}(0,0)(-5,-15)
1798 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1799 \end{picture}
1800 \begin{picture}(0,0)(-55,-15)
1801 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1802 \end{picture}
1803 \begin{picture}(0,0)(12.5,-5)
1804 \includegraphics[width=1cm]{100_arrow.eps}
1805 \end{picture}
1806 \begin{picture}(0,0)(90,-15)
1807 \includegraphics[height=0.9cm]{010_arrow.eps}
1808 \end{picture}
1809 \end{center}
1810 \end{minipage}
1811 }\\[0.1cm]
1812
1813 \begin{minipage}{5.9cm}
1814 Erhart/Albe results
1815 \begin{itemize}
1816  \item Lowest activation energy: $\approx$ 2.2 eV
1817  \item 2.4 times higher than VASP
1818  \item Different pathway
1819 \end{itemize}
1820 \end{minipage}
1821
1822 \end{minipage}
1823 \begin{minipage}{6.5cm}
1824
1825 \framebox{
1826 \begin{minipage}{5.9cm}
1827 %\begin{flushright}
1828 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1829 %\end{flushright}
1830 %\begin{center}
1831 %\begin{pspicture}(0,0)(0,0)
1832 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1833 %\end{pspicture}
1834 %\begin{picture}(0,0)(60,-5)
1835 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1836 %\end{picture}
1837 %\begin{picture}(0,0)(0,-5)
1838 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1839 %\end{picture}
1840 %\begin{picture}(0,0)(-55,-5)
1841 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1842 %\end{picture}
1843 %\begin{picture}(0,0)(12.5,5)
1844 %\includegraphics[width=1cm]{100_arrow.eps}
1845 %\end{picture}
1846 %\begin{picture}(0,0)(90,0)
1847 %\includegraphics[height=0.9cm]{001_arrow.eps}
1848 %\end{picture}
1849 %\end{center}
1850 %\vspace{0.2cm}
1851 %\end{minipage}
1852 %}\\[0.2cm]
1853 %
1854 %\framebox{
1855 %\begin{minipage}{5.9cm}
1856 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1857 \end{minipage}
1858 }\\[0.1cm]
1859
1860 \begin{minipage}{5.9cm}
1861 Transition involving \ci{} \hkl<1 1 0>
1862 \begin{itemize}
1863  \item Bond-centered configuration unstable\\
1864        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1865  \item Transition minima of path 2 \& 3\\
1866        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1867  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1868  \item 2.4 - 3.4 times higher than VASP
1869  \item Rotation of dumbbell orientation
1870 \end{itemize}
1871 \vspace{0.1cm}
1872 \begin{center}
1873 {\color{blue}Overestimated diffusion barrier}
1874 \end{center}
1875 \end{minipage}
1876
1877 \end{minipage}
1878
1879 \end{slide}
1880
1881 \begin{slide}
1882
1883  {\large\bf\boldmath
1884   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1885  }
1886
1887 \small
1888
1889 \vspace*{0.1cm}
1890
1891 Binding energy:
1892 $
1893 E_{\text{b}}=
1894 E_{\text{f}}^{\text{defect combination}}-
1895 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1896 E_{\text{f}}^{\text{2nd defect}}
1897 $
1898
1899 \vspace*{0.1cm}
1900
1901 {\scriptsize
1902 \begin{tabular}{l c c c c c c}
1903 \hline
1904  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1905  \hline
1906  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1907  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1908  \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1909  \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1910  \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1911  \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1912  \hline
1913  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1914  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1915 \hline
1916 \end{tabular}
1917 }
1918
1919 \vspace*{0.3cm}
1920
1921 \footnotesize
1922
1923 \begin{minipage}[t]{3.8cm}
1924 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1925 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1926 \end{minipage}
1927 \begin{minipage}[t]{3.5cm}
1928 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1929 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1930 \end{minipage}
1931 \begin{minipage}[t]{5.5cm}
1932 \begin{itemize}
1933  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1934        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1935  \item Stress compensation / increase
1936  \item Unfavored: antiparallel orientations
1937  \item Indication of energetically favored\\
1938        agglomeration
1939  \item Most favorable: C clustering
1940  \item However: High barrier ($>4\,\text{eV}$)
1941  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1942        (Entropy)
1943 \end{itemize}
1944 \end{minipage}
1945
1946 \begin{picture}(0,0)(-295,-130)
1947 \includegraphics[width=3.5cm]{comb_pos.eps}
1948 \end{picture}
1949
1950 \end{slide}
1951
1952 \begin{slide}
1953
1954  {\large\bf\boldmath
1955   Combinations of C-Si \hkl<1 0 0>-type interstitials
1956  }
1957
1958 \small
1959
1960 \vspace*{0.1cm}
1961
1962 Energetically most favorable combinations along \hkl<1 1 0>
1963
1964 \vspace*{0.1cm}
1965
1966 {\scriptsize
1967 \begin{tabular}{l c c c c c c}
1968 \hline
1969  & 1 & 2 & 3 & 4 & 5 & 6\\
1970 \hline
1971 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1972 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1973 Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
1974 \hline
1975 \end{tabular}
1976 }
1977
1978 \vspace*{0.3cm}
1979
1980 \begin{minipage}{7.0cm}
1981 \includegraphics[width=7cm]{db_along_110_cc.ps}
1982 \end{minipage}
1983 \begin{minipage}{6.0cm}
1984 \begin{itemize}
1985  \item Interaction proportional to reciprocal cube of C-C distance
1986  \item Saturation in the immediate vicinity
1987  \renewcommand\labelitemi{$\Rightarrow$}
1988  \item Agglomeration of \ci{} expected
1989  \item Absence of C clustering
1990 \end{itemize}
1991 \begin{center}
1992 {\color{blue}
1993  Consisten with initial precipitation model
1994 }
1995 \end{center}
1996 \end{minipage}
1997
1998 \vspace{0.2cm}
1999
2000 \end{slide}
2001
2002 \begin{slide}
2003
2004  {\large\bf\boldmath
2005   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
2006  }
2007
2008  \scriptsize
2009
2010 %\begin{center}
2011 %\begin{minipage}{3.2cm}
2012 %\includegraphics[width=3cm]{sub_110_combo.eps}
2013 %\end{minipage}
2014 %\begin{minipage}{7.8cm}
2015 %\begin{tabular}{l c c c c c c}
2016 %\hline
2017 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
2018 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
2019 %\hline
2020 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
2021 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
2022 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
2023 %4 & \RM{4} & B & D & E & E & D \\
2024 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
2025 %\hline
2026 %\end{tabular}
2027 %\end{minipage}
2028 %\end{center}
2029
2030 %\begin{center}
2031 %\begin{tabular}{l c c c c c c c c c c}
2032 %\hline
2033 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
2034 %\hline
2035 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
2036 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
2037 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
2038 %\hline
2039 %\end{tabular}
2040 %\end{center}
2041
2042 \begin{minipage}{6.0cm}
2043 \includegraphics[width=5.8cm]{c_sub_si110.ps}
2044 \end{minipage}
2045 \begin{minipage}{7cm}
2046 \scriptsize
2047 \begin{itemize}
2048  \item IBS: C may displace Si\\
2049        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
2050  \item Assumption:\\
2051        \hkl<1 1 0>-type $\rightarrow$ favored combination
2052  \renewcommand\labelitemi{$\Rightarrow$}
2053  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
2054  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
2055  \item Interaction drops quickly to zero\\
2056        $\rightarrow$ low capture radius
2057 \end{itemize}
2058 \begin{center}
2059  {\color{blue}
2060  IBS process far from equilibrium\\
2061  \cs{} \& \si{} instead of thermodynamic ground state
2062  }
2063 \end{center}
2064 \end{minipage}
2065
2066 \begin{minipage}{6.5cm}
2067 \includegraphics[width=6.0cm]{162-097.ps}
2068 \begin{itemize}
2069  \item Low migration barrier
2070 \end{itemize}
2071 \end{minipage}
2072 \begin{minipage}{6.5cm}
2073 \begin{center}
2074 Ab initio MD at \degc{900}\\
2075 \includegraphics[width=3.3cm]{md_vasp_01.eps}
2076 $t=\unit[2230]{fs}$\\
2077 \includegraphics[width=3.3cm]{md_vasp_02.eps}
2078 $t=\unit[2900]{fs}$
2079 \end{center}
2080 {\color{blue}
2081 Contribution of entropy to structural formation
2082 }
2083 \end{minipage}
2084
2085 \end{slide}
2086
2087 \begin{slide}
2088
2089  {\large\bf\boldmath
2090   Migration in C-Si \hkl<1 0 0> and vacancy combinations
2091  }
2092
2093  \footnotesize
2094
2095 \vspace{0.1cm}
2096
2097 \begin{minipage}[t]{3cm}
2098 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2099 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2100 \end{minipage}
2101 \begin{minipage}[t]{7cm}
2102 \vspace{0.2cm}
2103 \begin{center}
2104  Low activation energies\\
2105  High activation energies for reverse processes\\
2106  $\Downarrow$\\
2107  {\color{blue}C$_{\text{sub}}$ very stable}\\
2108 \vspace*{0.1cm}
2109  \hrule
2110 \vspace*{0.1cm}
2111  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2112  $\Downarrow$\\
2113  {\color{blue}Formation of SiC by successive substitution by C}
2114
2115 \end{center}
2116 \end{minipage}
2117 \begin{minipage}[t]{3cm}
2118 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2119 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2120 \end{minipage}
2121
2122
2123 \framebox{
2124 \begin{minipage}{5.9cm}
2125 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2126 \begin{center}
2127 \begin{picture}(0,0)(70,0)
2128 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2129 \end{picture}
2130 \begin{picture}(0,0)(30,0)
2131 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2132 \end{picture}
2133 \begin{picture}(0,0)(-10,0)
2134 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2135 \end{picture}
2136 \begin{picture}(0,0)(-48,0)
2137 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2138 \end{picture}
2139 \begin{picture}(0,0)(12.5,5)
2140 \includegraphics[width=1cm]{100_arrow.eps}
2141 \end{picture}
2142 \begin{picture}(0,0)(97,-10)
2143 \includegraphics[height=0.9cm]{001_arrow.eps}
2144 \end{picture}
2145 \end{center}
2146 \vspace{0.1cm}
2147 \end{minipage}
2148 }
2149 \begin{minipage}{0.3cm}
2150 \hfill
2151 \end{minipage}
2152 \framebox{
2153 \begin{minipage}{5.9cm}
2154 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2155 \begin{center}
2156 \begin{picture}(0,0)(60,0)
2157 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2158 \end{picture}
2159 \begin{picture}(0,0)(25,0)
2160 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2161 \end{picture}
2162 \begin{picture}(0,0)(-20,0)
2163 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2164 \end{picture}
2165 \begin{picture}(0,0)(-55,0)
2166 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2167 \end{picture}
2168 \begin{picture}(0,0)(12.5,5)
2169 \includegraphics[width=1cm]{100_arrow.eps}
2170 \end{picture}
2171 \begin{picture}(0,0)(95,0)
2172 \includegraphics[height=0.9cm]{001_arrow.eps}
2173 \end{picture}
2174 \end{center}
2175 \vspace{0.1cm}
2176 \end{minipage}
2177 }
2178
2179 \end{slide}
2180
2181 \begin{slide}
2182
2183  {\large\bf
2184   Conclusion of defect / migration / combined defect simulations
2185  }
2186
2187  \footnotesize
2188
2189 \vspace*{0.1cm}
2190
2191 Defect structures
2192 \begin{itemize}
2193  \item Accurately described by quantum-mechanical simulations
2194  \item Less accurate description by classical potential simulations
2195  \item Underestimated formation energy of \cs{} by classical approach
2196  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2197 \end{itemize}
2198
2199 Migration
2200 \begin{itemize}
2201  \item C migration pathway in Si identified
2202  \item Consistent with reorientation and diffusion experiments
2203 \end{itemize}
2204 \begin{itemize}
2205  \item Different path and ...
2206  \item overestimated barrier by classical potential calculations
2207 \end{itemize}
2208
2209 Concerning the precipitation mechanism
2210 \begin{itemize}
2211  \item Agglomeration of C-Si dumbbells energetically favorable
2212        (stress compensation)
2213  \item C-Si indeed favored compared to
2214        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2215  \item Possible low interaction capture radius of
2216        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2217  \item Low barrier for
2218        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2219  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2220        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2221 \end{itemize}
2222 \begin{center}
2223 {\color{blue}Results suggest increased participation of \cs}
2224 \end{center}
2225
2226 \end{slide}
2227
2228 \begin{slide}
2229
2230  {\large\bf
2231   Silicon carbide precipitation simulations
2232  }
2233
2234  \small
2235
2236 {\scriptsize
2237  \begin{pspicture}(0,0)(12,6.5)
2238   % nodes
2239   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2240    \parbox{7cm}{
2241    \begin{itemize}
2242     \item Create c-Si volume
2243     \item Periodc boundary conditions
2244     \item Set requested $T$ and $p=0\text{ bar}$
2245     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2246    \end{itemize}
2247   }}}}
2248   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2249    \parbox{7cm}{
2250    Insertion of C atoms at constant T
2251    \begin{itemize}
2252     \item total simulation volume {\pnode{in1}}
2253     \item volume of minimal SiC precipitate {\pnode{in2}}
2254     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2255           precipitate
2256    \end{itemize}
2257   }}}}
2258   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2259    \parbox{7.0cm}{
2260    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2261   }}}}
2262   \ncline[]{->}{init}{insert}
2263   \ncline[]{->}{insert}{cool}
2264   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2265   \rput(7.8,6){\footnotesize $V_1$}
2266   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2267   \rput(9.2,4.85){\tiny $V_2$}
2268   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2269   \rput(9.55,4.45){\footnotesize $V_3$}
2270   \rput(7.9,3.2){\pnode{ins1}}
2271   \rput(9.22,2.8){\pnode{ins2}}
2272   \rput(11.0,2.4){\pnode{ins3}}
2273   \ncline[]{->}{in1}{ins1}
2274   \ncline[]{->}{in2}{ins2}
2275   \ncline[]{->}{in3}{ins3}
2276  \end{pspicture}
2277 }
2278
2279 \begin{itemize}
2280  \item Restricted to classical potential simulations
2281  \item $V_2$ and $V_3$ considered due to low diffusion
2282  \item Amount of C atoms: 6000
2283        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2284  \item Simulation volume: $31\times 31\times 31$ unit cells
2285        (238328 Si atoms)
2286 \end{itemize}
2287
2288 \end{slide}
2289
2290 \begin{slide}
2291
2292  {\large\bf\boldmath
2293   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2294  }
2295
2296  \small
2297
2298 \begin{minipage}{6.5cm}
2299 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2300 \end{minipage}
2301 \begin{minipage}{6.5cm}
2302 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2303 \end{minipage}
2304
2305 \begin{minipage}{6.5cm}
2306 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2307 \end{minipage}
2308 \begin{minipage}{6.5cm}
2309 \scriptsize
2310 \underline{Low C concentration ($V_1$)}\\
2311 \hkl<1 0 0> C-Si dumbbell dominated structure
2312 \begin{itemize}
2313  \item Si-C bumbs around 0.19 nm
2314  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2315        concatenated dumbbells of various orientation
2316  \item Si-Si NN distance stretched to 0.3 nm
2317 \end{itemize}
2318 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2319 \underline{High C concentration ($V_2$, $V_3$)}\\
2320 High amount of strongly bound C-C bonds\\
2321 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2322 Only short range order observable\\
2323 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2324 \end{minipage}
2325
2326 \end{slide}
2327
2328 \begin{slide}
2329
2330  {\large\bf\boldmath
2331   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2332  }
2333
2334  \small
2335
2336 \begin{minipage}{6.5cm}
2337 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2338 \end{minipage}
2339 \begin{minipage}{6.5cm}
2340 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2341 \end{minipage}
2342
2343 \begin{minipage}{6.5cm}
2344 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2345 \end{minipage}
2346 \begin{minipage}{6.5cm}
2347 \scriptsize
2348 \underline{Low C concentration ($V_1$)}\\
2349 \hkl<1 0 0> C-Si dumbbell dominated structure
2350 \begin{itemize}
2351  \item Si-C bumbs around 0.19 nm
2352  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2353        concatenated dumbbells of various orientation
2354  \item Si-Si NN distance stretched to 0.3 nm
2355 \end{itemize}
2356 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2357 \underline{High C concentration ($V_2$, $V_3$)}\\
2358 High amount of strongly bound C-C bonds\\
2359 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2360 Only short range order observable\\
2361 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2362 \end{minipage}
2363
2364 \begin{pspicture}(0,0)(0,0)
2365 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2366 \begin{minipage}{10cm}
2367 \small
2368 {\color{red}\bf 3C-SiC formation fails to appear}
2369 \begin{itemize}
2370 \item Low C concentration simulations
2371  \begin{itemize}
2372   \item Formation of \ci{} indeed occurs
2373   \item Agllomeration not observed
2374  \end{itemize}
2375 \item High C concentration simulations
2376  \begin{itemize}
2377   \item Amorphous SiC-like structure\\
2378         (not expected at prevailing temperatures)
2379   \item Rearrangement and transition into 3C-SiC structure missing
2380  \end{itemize}
2381 \end{itemize}
2382 \end{minipage}
2383  }}}
2384 \end{pspicture}
2385
2386 \end{slide}
2387
2388 \begin{slide}
2389
2390  {\large\bf
2391   Limitations of molecular dynamics and short range potentials
2392  }
2393
2394 \footnotesize
2395
2396 \vspace{0.2cm}
2397
2398 \underline{Time scale problem of MD}\\[0.2cm]
2399 Minimize integration error\\
2400 $\Rightarrow$ discretization considerably smaller than
2401               reciprocal of fastest vibrational mode\\[0.1cm]
2402 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2403 $\Rightarrow$ suitable choice of time step:
2404               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2405 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2406 Several local minima in energy surface separated by large energy barriers\\
2407 $\Rightarrow$ transition event corresponds to a multiple
2408               of vibrational periods\\
2409 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2410               infrequent transition events\\[0.1cm]
2411 {\color{blue}Accelerated methods:}
2412 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2413
2414 \vspace{0.3cm}
2415
2416 \underline{Limitations related to the short range potential}\\[0.2cm]
2417 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2418 and 2$^{\text{nd}}$ next neighbours\\
2419 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2420
2421 \vspace{0.3cm}
2422
2423 \framebox{
2424 \color{red}
2425 Potential enhanced problem of slow phase space propagation
2426 }
2427
2428 \vspace{0.3cm}
2429
2430 \underline{Approach to the (twofold) problem}\\[0.2cm]
2431 Increased temperature simulations without TAD corrections\\
2432 (accelerated methods or higher time scales exclusively not sufficient)
2433
2434 \begin{picture}(0,0)(-260,-30)
2435 \framebox{
2436 \begin{minipage}{4.2cm}
2437 \tiny
2438 \begin{center}
2439 \vspace{0.03cm}
2440 \underline{IBS}
2441 \end{center}
2442 \begin{itemize}
2443 \item 3C-SiC also observed for higher T
2444 \item higher T inside sample
2445 \item structural evolution vs.\\
2446       equilibrium properties
2447 \end{itemize}
2448 \end{minipage}
2449 }
2450 \end{picture}
2451
2452 \begin{picture}(0,0)(-305,-155)
2453 \framebox{
2454 \begin{minipage}{2.5cm}
2455 \tiny
2456 \begin{center}
2457 retain proper\\
2458 thermodynmic sampling
2459 \end{center}
2460 \end{minipage}
2461 }
2462 \end{picture}
2463
2464 \end{slide}
2465
2466 \begin{slide}
2467
2468  {\large\bf
2469   Increased temperature simulations at low C concentration
2470  }
2471
2472 \small
2473
2474 \begin{minipage}{6.5cm}
2475 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2476 \end{minipage}
2477 \begin{minipage}{6.5cm}
2478 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2479 \end{minipage}
2480
2481 \begin{minipage}{6.5cm}
2482 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2483 \end{minipage}
2484 \begin{minipage}{6.5cm}
2485 \scriptsize
2486  \underline{Si-C bonds:}
2487  \begin{itemize}
2488   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2489   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2490  \end{itemize}
2491  \underline{Si-Si bonds:}
2492  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2493  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2494  \underline{C-C bonds:}
2495  \begin{itemize}
2496   \item C-C next neighbour pairs reduced (mandatory)
2497   \item Peak at 0.3 nm slightly shifted
2498         \begin{itemize}
2499          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2500                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2501                combinations (|)\\
2502                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2503                ($\downarrow$)
2504          \item Range [|-$\downarrow$]:
2505                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2506                with nearby Si$_{\text{I}}$}
2507         \end{itemize}
2508  \end{itemize}
2509 \end{minipage}
2510
2511 \begin{picture}(0,0)(-330,-74)
2512 \color{blue}
2513 \framebox{
2514 \begin{minipage}{1.6cm}
2515 \tiny
2516 \begin{center}
2517 stretched SiC\\[-0.1cm]
2518 in c-Si
2519 \end{center}
2520 \end{minipage}
2521 }
2522 \end{picture}
2523
2524 \end{slide}
2525
2526 \begin{slide}
2527
2528  {\large\bf
2529   Increased temperature simulations at low C concentration
2530  }
2531
2532 \small
2533
2534 \begin{minipage}{6.5cm}
2535 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2536 \end{minipage}
2537 \begin{minipage}{6.5cm}
2538 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2539 \end{minipage}
2540
2541 \begin{minipage}{6.5cm}
2542 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2543 \end{minipage}
2544 \begin{minipage}{6.5cm}
2545 \scriptsize
2546  \underline{Si-C bonds:}
2547  \begin{itemize}
2548   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2549   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2550  \end{itemize}
2551  \underline{Si-Si bonds:}
2552  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2553  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2554  \underline{C-C bonds:}
2555  \begin{itemize}
2556   \item C-C next neighbour pairs reduced (mandatory)
2557   \item Peak at 0.3 nm slightly shifted
2558         \begin{itemize}
2559          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2560                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2561                combinations (|)\\
2562                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2563                ($\downarrow$)
2564          \item Range [|-$\downarrow$]:
2565                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2566                with nearby Si$_{\text{I}}$}
2567         \end{itemize}
2568  \end{itemize}
2569 \end{minipage}
2570
2571 %\begin{picture}(0,0)(-330,-74)
2572 %\color{blue}
2573 %\framebox{
2574 %\begin{minipage}{1.6cm}
2575 %\tiny
2576 %\begin{center}
2577 %stretched SiC\\[-0.1cm]
2578 %in c-Si
2579 %\end{center}
2580 %\end{minipage}
2581 %}
2582 %\end{picture}
2583
2584 \begin{pspicture}(0,0)(0,0)
2585 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2586 \begin{minipage}{10cm}
2587 \small
2588 {\color{blue}\bf Stretched SiC in c-Si}
2589 \begin{itemize}
2590 \item Consistent to precipitation model involving \cs{}
2591 \item Explains annealing behavior of high/low T C implants
2592       \begin{itemize}
2593        \item Low T: highly mobiel \ci{}
2594        \item High T: stable configurations of \cs{}
2595       \end{itemize}
2596 \end{itemize}
2597 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2598 $\Rightarrow$ Precipitation mechanism involving \cs{}
2599 \end{minipage}
2600  }}}
2601 \end{pspicture}
2602
2603 \end{slide}
2604
2605 \begin{slide}
2606
2607  {\large\bf
2608   Increased temperature simulations at high C concentration
2609  }
2610
2611 \footnotesize
2612
2613 \begin{minipage}{6.5cm}
2614 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2615 \end{minipage}
2616 \begin{minipage}{6.5cm}
2617 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2618 \end{minipage}
2619
2620 \vspace{0.1cm}
2621
2622 \scriptsize
2623
2624 \framebox{
2625 \begin{minipage}[t]{6.0cm}
2626 0.186 nm: Si-C pairs $\uparrow$\\
2627 (as expected in 3C-SiC)\\[0.2cm]
2628 0.282 nm: Si-C-C\\[0.2cm]
2629 $\approx$0.35 nm: C-Si-Si
2630 \end{minipage}
2631 }
2632 \begin{minipage}{0.2cm}
2633 \hfill
2634 \end{minipage}
2635 \framebox{
2636 \begin{minipage}[t]{6.0cm}
2637 0.15 nm: C-C pairs $\uparrow$\\
2638 (as expected in graphite/diamond)\\[0.2cm]
2639 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2640 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2641 \end{minipage}
2642 }
2643
2644 \begin{itemize}
2645 \item Decreasing cut-off artifact
2646 \item {\color{red}Amorphous} SiC-like phase remains
2647 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2648 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2649 \end{itemize}
2650
2651 \vspace{-0.1cm}
2652
2653 \begin{center}
2654 {\color{blue}
2655 \framebox{
2656 {\color{black}
2657 High C \& small $V$ \& short $t$
2658 $\Rightarrow$
2659 }
2660 Slow restructuring due to strong C-C bonds
2661 {\color{black}
2662 $\Leftarrow$
2663 High C \& low T implants
2664 }
2665 }
2666 }
2667 \end{center}
2668
2669 \end{slide}
2670
2671 \begin{slide}
2672
2673  {\large\bf
2674   Summary and Conclusions
2675  }
2676
2677  \scriptsize
2678
2679 %\vspace{0.1cm}
2680
2681 \framebox{
2682 \begin{minipage}[t]{12.9cm}
2683  \underline{Pecipitation simulations}
2684  \begin{itemize}
2685   \item High C concentration $\rightarrow$ amorphous SiC like phase
2686   \item Problem of potential enhanced slow phase space propagation
2687   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2688   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2689   \item High T necessary to simulate IBS conditions (far from equilibrium)
2690   \item Precipitation by successive agglomeration of \cs (epitaxy)
2691   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2692         (stretched SiC, interface)
2693  \end{itemize}
2694 \end{minipage}
2695 }
2696
2697 %\vspace{0.1cm}
2698
2699 \framebox{
2700 \begin{minipage}{12.9cm}
2701  \underline{Defects}
2702  \begin{itemize}
2703    \item DFT / EA
2704         \begin{itemize}
2705          \item Point defects excellently / fairly well described
2706                by DFT / EA
2707          \item C$_{\text{sub}}$ drastically underestimated by EA
2708          \item EA predicts correct ground state:
2709                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2710          \item Identified migration path explaining
2711                diffusion and reorientation experiments by DFT
2712          \item EA fails to describe \ci{} migration:
2713                Wrong path \& overestimated barrier
2714         \end{itemize}
2715    \item Combinations of defects
2716          \begin{itemize}
2717           \item Agglomeration of point defects energetically favorable
2718                 by compensation of stress
2719           \item Formation of C-C unlikely
2720           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2721           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2722                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2723         \end{itemize}
2724  \end{itemize}
2725 \end{minipage}
2726 }
2727
2728 \begin{center}
2729 {\color{blue}
2730 \framebox{Precipitation by successive agglomeration of \cs{}}
2731 }
2732 \end{center}
2733
2734 \end{slide}
2735
2736 \begin{slide}
2737
2738  {\large\bf
2739   Acknowledgements
2740  }
2741
2742  \vspace{0.1cm}
2743
2744  \small
2745
2746  Thanks to \ldots
2747
2748  \underline{Augsburg}
2749  \begin{itemize}
2750   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2751   \item Ralf Utermann (EDV)
2752  \end{itemize}
2753
2754  \underline{Helsinki}
2755  \begin{itemize}
2756   \item Prof. K. Nordlund (MD)
2757  \end{itemize}
2758
2759  \underline{Munich}
2760  \begin{itemize}
2761   \item Bayerische Forschungsstiftung (financial support)
2762  \end{itemize}
2763
2764  \underline{Paderborn}
2765  \begin{itemize}
2766   \item Prof. J. Lindner (SiC)
2767   \item Prof. G. Schmidt (DFT + financial support)
2768   \item Dr. E. Rauls (DFT + SiC)
2769   \item Dr. S. Sanna (VASP)
2770  \end{itemize}
2771
2772 \vspace{0.2cm}
2773
2774 \begin{center}
2775 \framebox{
2776 \bf Thank you for your attention!
2777 }
2778 \end{center}
2779
2780 \end{slide}
2781
2782 \end{document}
2783
2784 \fi